The Bokanovsky process in Brave New World is basically cloning. With one egg dipped in the sperm solution at the hatchery building, fertilizers can create up to 96 identical human beings.
Being able to control the population of the world like this contributes to social stability because the controllers can always make sure they have enough gammas, deltas and epsilons available to do the work that has to be done at each caste level of society.
Without the ability to control the numbers of people in each caste, world leaders would be at the mercy of fate, disease, or conflict when it comes to world population. For example, let's say it takes 20,000 epsilons to man the waste stations. However, a deadly disease one year wiped out 1/2 of them. This would leave the socity unstable, because there wouldn't be enough workers to complete the tasks necessary to keep the society running.
With Bokanovsky, however, if disease wiped out a good segment of a class, they could pop out batches of 96 clones in a relatively short period of time, restoring social order and making enough people to complete the jobs that need to be done.